% Newton iteration near a simple root & a double root
% Convergence is quadratic for simple root
% Convergence is linear for double root
% See example 5.11 on p.231 of Heath
% NewtonDoubleRoot.m
% function 1 has simple roots at x=1 & -1: f1(x)=x^2-1
% function 2 has double root at x=1: f2(x)=x^2-2*x+1
% initial guess: x0=3
% tolerance: tol=1e-6
% K. Ming Leung, 02/13/03

clear all; format long; tol=1e-6;
x1=2; x2=x1; loop=0;
disp([loop x1 x2]);
for loop=1:5
    f1x=x1*x1-1; f2x=x2*x2-2*x2+1;
    f1p=2*x1; f2p=2*x2-2;
    x1=x1-f1x/f1p; x2=x2-f2x/f2p;
disp([loop x1 x2]);
end;